Thermoeconomic cost optimization of superconducting magnets for proton therapy gantries

Abstract

A compact gantry delivering 70-220 MeV protons with fixed field in the superconducting magnets could reduce the cost and improve the adoption of proton therapy. While a number of magnet and cryogenics designs have been proposed, the combined capital and operating costs of state-of-the-art superconducting materials have not been analyzed. In response, we develop a thermoeconomic model of a multi-stage, conduction cooled gantry lattice and analyze the cryocooler operating cost, cryocooler capital cost and conductor capital cost for Nb-Ti, Nb 3 Sn, REBCO and Bi-2223 over a continuous range of magnet temperatures, and a differential evolution algorithm is used to identify the optimal combination of thermal intercept temperatures. Although Nb 3 Sn yields the lowest Net Present Value (NPV) of $111.7k at a magnet temperature of 9.4 K, the optimized Bi-2223 design at 12.8 K approaches the realm of commercial feasibility by offering improved thermal stability and forgoing the need for costly conductor heat treatment and magnet quench training. Furthermore, it was found that Nb 3 Sn was more cost effective than Nb-Ti and that REBCO was not economically viable for the parameters of this investigation. The thermoeconomic model developed herein can optimize conductor choices, magnet temperatures and thermal staging which has value for any conduction-cooled superconducting magnet.

High temperature superconductors for commercial magnets

“…[56] and the references therein). Traditionally, mostly LTS are applied, but more recently studies have emerged to investigate the feasibility of HTS for these applications (figure 6(g)) [56,57,[66][67][68][69]. Also here, a preference is seen for cryogen-free use of superconducting technologies, for which HTS lends itself much better than LTS.…”

“…For commercial applications, the conductor cost has to be considered in relation to the overall capital-and operating-cost over the lifetime of the application. An attempt to analyze this in detail was recently published by Teyber et al [67]. In this work, a thermo-economic model of an achromatic main bendmagnet for proton therapy [117] is used to analyze the total cost over an assumed 20 year lifespan of the application.…”

“…Although Bi-2212 has not been included in the analyses in the original article [67], one can speculate how the overall cost for this material will compare. The conductor price-per-kAm of Bi-2212 is lower than for Bi-2223 despite the higher per-kg price, due to the higher current-density, while the temperature margin of Bi-2223 is higher (figure 31), which likely leads to increased cooling-cost for Bi-2212.…”

“…It can be argued that a magnetic field of, say, 7 T will cover a large fraction of emerging commercial applications Selected outcomes of a thermo-economic cost model for a cryogen-free main bend magnet for a gantry for proton therapy. Reproduced from [67]. © IOP Publishing Ltd All rights reserved.…”

Mechanical and Thermal Analysis of an HTS Superconducting Magnet for an Achromatic Gantry for Proton Therapy

“…The innovative concept of using a combination of two identical superconducting bend magnets working at a fixed field in a proton therapy gantry, allows for a light and compact design, while being able to deliver protons over a range of 70 to 220 MeV, and is a further simplification of the design presented in [2]. The proposed concept uses the hightemperature superconductor (HTS) Bi-2223, as it has been shown to be competitive in terms of reduced manufacturing cost and improved thermal stability [3], [4]. The new design, as an HTS technology demonstrator, further simplifies the coil design, reducing the field and increasing the weight as a tradeoff.…”